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Characterizing proximity trees

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Abstract

Complete characterizations are given for those trees that can be drawn as either the relative neighborhood graph, relatively closest graph, Gabriel graph, or modified Gabriel graph of a set of points in the plane. The characterizations give rise to linear-time algorithms for determining whether a tree has such a drawing; if such a drawing exists one can be constructed in linear time in the real RAM model. The characterization of Gabriel graphs settles several conjectures of Matula and Sokal [17].

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Author information

Authors and Affiliations

  1. Département de Mathématiques et Informatique, Université du Québec à Trois-Rivières, C.P. 500, G9A 5H7, Trois-Rivières, Québec, Canada

    P. Bose

  2. Department of Computer Science, Williams College, 01267, Williamstown, MA, USA

    W. Lenhart

  3. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, via Salaria 113, I-00198, Roma, Italia

    G. Liotta

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  1. P. Bose
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  2. W. Lenhart
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  3. G. Liotta
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Additional information

Communicated by G. Di Battista and R. Tamassia.

This research was conducted while the author was at the School of Computer Science of McGill University. Research supported in part by NSERC and FCAR.

This work was done when this author was visiting the School of Computer Science of McGill University.

This work was done when this author was visiting the School of Computer Science of McGill University.

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Bose, P., Lenhart, W. & Liotta, G. Characterizing proximity trees. Algorithmica 16, 83–110 (1996). https://doi.org/10.1007/BF02086609

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  • DOI: https://doi.org/10.1007/BF02086609

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